David Letterman jokes, apologizes on Monday's show

David Letterman apologized to his wife on Monday's "Late Show, saying she had been "horribly hurt by my behavior."

The late-night host vowed to repair his relationship with his wife, Regina Lasko.

"Let me tell you folks, I got my work cut out for me," he said, according to an early transcript of the program released by CBS.

CBS via The Associated PressMartin Short, left, and Steve Martin joke with David Letterman during a taping of 'The Late Show with David Letterman, ' on Monday in New York.

Monday's show was the first Letterman had taped since Thursday, when he disclosed that he had had sexual relationships with women who worked for him and said that he had been the victim of a $2 million blackmail threat. During the hour, he also apologized to his staff.

He arrived on stage to applause and cheers from his studio audience. After drinking it in, he grinned sheepishly and inquired, with a mock stammer, "Did your, did your weekend just fly by?"

After pausing for the audience's sympathetic laughter, he went on: "I mean, I'll be honest with you folks -- right now, I would give anything to be hiking on the Appalachian Trail."

"I got into the car this morning, " he added, "and the navigation lady wasn't speaking to me. Ouch."

In a more somber display, Letterman voiced his mea culpas. Regarding his wife, he said that, "if you hurt a person and it's your responsibility, you try to fix it."

As Letterman faced Monday's show, and the shows that will come after, it was clear that how he deals with his messy situation could prove to be a defining chapter in his long TV career. And, with any luck, it could clinch his recent ratings victory in late-night TV.

While Letterman has joked about his affairs with female staffers, it is unclear how many women he had sex with, and he has offered no specifics.

But one of his affairs was with Stephanie Birkitt, who was an assistant to Letterman and frequently appeared on camera with the host in comedy bits. Birkitt went on to live with Robert Halderman, a CBS News producer, who found her diary describing her relationship with Letterman and used it to help blackmail him, a law enforcement official confirmed Monday. The official spoke on the condition of anonymity because the investigation is ongoing.

Halderman, a producer for the true-crime show "48 Hours Mystery," pleaded innocent last week to extortion charges.